Internal problem ID [10255]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 9, system of higher order odes
Problem number: 1933.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-\frac {y \left (t \right ) z \left (t \right )}{2}+\frac {x \left (t \right ) y \left (t \right )}{2}+\frac {x \left (t \right ) z \left (t \right )}{2}\\ y^{\prime }\left (t \right )&=\frac {y \left (t \right ) z \left (t \right )}{2}+\frac {x \left (t \right ) y \left (t \right )}{2}-\frac {x \left (t \right ) z \left (t \right )}{2}\\ z^{\prime }\left (t \right )&=-\frac {x \left (t \right ) y \left (t \right )}{2}+\frac {x \left (t \right ) z \left (t \right )}{2}+\frac {y \left (t \right ) z \left (t \right )}{2} \end {align*}
✓ Solution by Maple
Time used: 0.954 (sec). Leaf size: 4316
dsolve([diff(x(t),t)+diff(y(t),t)=x(t)*y(t),diff(y(t),t)+diff(z(t),t)=y(t)*z(t),diff(x(t),t)+diff(z(t),t)=x(t)*z(t)],singsol=all)
\begin{align*} \left [\left \{x \left (t \right ) &= \frac {2}{2 c_{2} -t}\right \}, \left \{y \left (t \right ) &= \left (\int -\frac {x \left (t \right )^{2} {\mathrm e}^{-\left (\int x \left (t \right )d t \right )}}{2}d t +c_{1} \right ) {\mathrm e}^{\int x \left (t \right )d t}\right \}, \{z \left (t \right ) = x \left (t \right )\}\right ] \\ \left [\left \{x \left (t \right ) &= \frac {2}{2 c_{2} -t}\right \}, \{y \left (t \right ) = x \left (t \right )\}, \left \{z \left (t \right ) &= \left (\int -\frac {x \left (t \right )^{2} {\mathrm e}^{-\left (\int x \left (t \right )d t \right )}}{2}d t +c_{1} \right ) {\mathrm e}^{\int x \left (t \right )d t}\right \}\right ] \\ \text {Expression too large to display} \\ \end{align*}
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[{x'[t]+y'[t]==x[t]*y[t],y'[t]+z'[t]==y[t]*z[t],x'[t]+z'[t]==x[t]*z[t]},{x[t],y[t],z[t]},t,IncludeSingularSolutions -> True]
Not solved